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Abstract

This article describes a technique which may be used to collect the information necessary to perform the full range cutting algorithm. The cutting algorithm is a means of bounding the signal probability and detection probability of faults in a combinational circuit. It allows an early identification of "hard to detect faults", and indicates where a circuit modification is required in order to meet a given test quality specification. There are two versions of the cutting algorithm: the full range, and the partial range. The difference between the two is that the full range is using intervals of [0,1], while the partial range is using shorter intervals. In order to perform the full range cutting algorithm, we have to collect the following information: (1) Identify the tree, and nontree lines.

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United States

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English (United States)

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Preanalysis for the Full Range Cutting Algorithm

This article describes a technique which may be used to collect
the information necessary to perform the full range cutting
algorithm. The cutting algorithm is a means of bounding the signal
probability and detection probability of faults in a combinational
circuit. It allows an early identification of "hard to detect
faults", and indicates where a circuit modification is required in
order to meet a given test quality specification. There are two
versions of the cutting algorithm: the full range, and the partial
range. The difference between the two is that the full range is using
intervals of [0,1], while the partial range is using shorter
intervals. In order to perform the full range cutting algorithm, we
have to collect the following information: (1) Identify the tree,
and nontree lines. (2) Identify the fanout branches that are cut
candidates. (3) Find the optimal cut, or nearly optimal cut. As
indicated by this title, the identification of all these items is
done by the same algorithm. Since the collection of tree lines and
nontree lines constitutes the set of all possible lines in the
circuit, it is only necessary to identify one of them. Thus, the
procedure we describe will identify the nontree lines. A line which
is not marked as a nontree line is, therefore, a tree line. To
illustrate the algorithm, consider the circuit of the figure. All
the lines in the circuit have been numbered. The algorithm calls for
propagating tokens from each individual fanout stem to the primary
outputs. Line 1 is a fanout stem, whose fanout branches are lines 7,
8, 9 and 10. The tokens T1, T2, T3 and T4 have been assigned to
the above fanout branches. These tokens are now propagated through
the network until the primary outputs are reached. The propagation
operation is a union over the tokens that were collected at the
block's inputs. For example, the set of tokens collected on line 42
is a union of the sets collected on its input lines 21, 32, and 33.

A line with multiple tokens assigned to it constitutes a nontree
line. Thus, the process of the fanout stem 1 has revealed that lines
27, 30, 31, 32, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47
and 48 are all nontree lines. Since these algorithm steps have to be
repeated for each fanout stem, all the other nontree lines, which are
not discovered by the first processing, will be discovered later. The
algorithm also identified the cut candidates. Fanout stem 1 splits
into 4 fanout branches: lines 7, 8, 9, and 10. It is always
possible to get by with a maximal cut - pattern which constitutes
cutting all the fanout branches, except for one. In the case of
fanout stem number 1, it would have been possible to get by with 3
cuts. However, by looking at the group of tokens collected at the
primary outputs it is possible to achieve a better cut, which will
lead to computation of tighter bounds. Consider the group of tokens
collected at primary output line 46...